IMHO "Cleared for takeoff" means just that. It's an ATC thing. Deciding to takeoff is in your hands. If you're happy then go, if not then pause. However, if on a single runway ops, and traffic at 2nm finals, one would trust that ATC 'know what they are doing and have taken everything into account'. If you don't go when it is safe then voices will be raised.
I've seen this happen, light behind heavy, that ATC said, "XYZ, in your own time cleared for takeoff." The light captain went ape-poo telling ATC he needed 2 mins etc. etc." ATC repeated, "in your one time........."
Interesting one about radar separation v timing. That's new to me. I thought radar spacing, on finals, was based on timing, hence everyone is at the same speed. How does that work on departure?